Mister Exam
Other calculators
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How to use it?
- Factor squared:
- y^4+9*y^2-6
- y^4-y^2-1
- y^4+9*y^2+2
- x^4-x^2+1
- Factor polynomial:
- x^5+x+1
- x^2-x-1
- x^4+x^2
- x^3+x+2
- Least common denominator:
- z/t-t/z
- z-8/z^2/3*z^(1/3)+4
- y/(y+3)^2-y/(y^2)-9
- ((x-x^3/6+x^5/120-x^7/5040)/(1-x^2/2+x^4/24-x^6/720))^5
- How do you in partial fractions?:
- (((z^2)+(6*z+4))/((z^3)+8))/(1/-1)
- (x^2-6*x-9)/(x-3)
- (x^2+x-6)/(x+2)
- (x^2+4*x+3)/(x+1)
- Derivative of:
-
x^4-x^2+1
- Factor polynomial:
- x^4-x^2+1
- Graphing y =:
- x^4-x^2+1
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Identical expressions
- x^ four -x^ two + one
- x to the power of 4 minus x squared plus 1
- x to the power of four minus x to the power of two plus one
- x4-x2+1
- x⁴-x²+1
- x to the power of 4-x to the power of 2+1
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Similar expressions
- x^4-x^2-1
- x^4+x^2+1
Factor x^4-x^2+1 squared
The solution
Factorization
[src]
/ ___\ / ___\ / ___ \ / ___\ | I \/ 3 | | I \/ 3 | | \/ 3 I| | I \/ 3 | |x + - + -----|*|x + - - + -----|*|x + - ----- + -|*|x + - - - -----| \ 2 2 / \ 2 2 / \ 2 2/ \ 2 2 /
$$\left(x + \left(\frac{\sqrt{3}}{2} - \frac{i}{2}\right)\right) \left(x + \left(\frac{\sqrt{3}}{2} + \frac{i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3}}{2} + \frac{i}{2}\right)\right) \left(x + \left(- \frac{\sqrt{3}}{2} - \frac{i}{2}\right)\right)$$
(((x + i/2 + sqrt(3)/2)*(x - i/2 + sqrt(3)/2))*(x - sqrt(3)/2 + i/2))*(x - i/2 - sqrt(3)/2)
The perfect square
Let's highlight the perfect square of the square three-member
$$\left(x^{4} - x^{2}\right) + 1$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x^{2} - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
$$\left(x^{4} - x^{2}\right) + 1$$
To do this, let's use the formula
$$a x^{4} + b x^{2} + c = a \left(m + x^{2}\right)^{2} + n$$
where
$$m = \frac{b}{2 a}$$
$$n = \frac{4 a c - b^{2}}{4 a}$$
In this case
$$a = 1$$
$$b = -1$$
$$c = 1$$
Then
$$m = - \frac{1}{2}$$
$$n = \frac{3}{4}$$
So,
$$\left(x^{2} - \frac{1}{2}\right)^{2} + \frac{3}{4}$$
Combining rational expressions
[src]
2 / 2\ 1 + x *\-1 + x /
$$x^{2} \left(x^{2} - 1\right) + 1$$
1 + x^2*(-1 + x^2)